Question

1. There are 10 questions on a true-false test. A student feels unprepared for this test and randomly guesses the answer for each of these.

1. What is the probability that student gets exactly 7 correct?
2. What is the probability that student gets exactly 8 correct?
3. What is the probability that student gets less than or equal 7 correct?
4. What is the probability that student gets more than 6 correct?

Answer 1

There are 10 questions on a true-false test. Therefore the probability of randomly guess answer of a question = 0.5,

n = number of questions = 10

Let X = total number of the correct answer.

Therefore, X follows binomial distribution with parameters n=10 and p=0.5

a) Here we want to find P( X = 7)

Let's use excel:

P(X = 7 ) = "=BINOMDIST(7,10,0.5,0)" = 0.1172

b) Here we want to find P( X = 8)

P(X = 8 ) = "=BINOMDIST(8,10,0.5,0)" = 0.0439

c)

Here we want to find P( X <= 7)

P(X <= 7 ) = "=BINOMDIST(7,10,0.5,1)" = 0.9453

d)

Here we want to find P( X > 6) = 1 - P( X <= 6) ....( 1 )

P(X <= 6 ) = "=BINOMDIST(6,10,0.5,1)" = 0.8281

Plug this value in equation ( 1 ), we get.

P( X > 6) = 1 - 0.8281 = 0.1719